Delayed Exponential Model Report

Stan Model

## S4 class stanmodel 'DE-modelSpec' coded as follows:
## data {
##   int<lower=0> N; // num observations
##   int<lower=0> ni; // num items
##   int<lower=0> ns; // num subjects
##   int<lower=0> nsi; // num subject-item combos
##   int<lower=0> si_lookup[ns, ni]; // lookup table for sparsely coded subject-item offsets
##   int<lower=0> nt; // num trials
##   int<lower=0> nc; // num strategies
##   real<lower=0> y[N]; // log RT 
##   int<lower=0> strategy[N]; // strategy for a given obs
##   int<lower=0> item[N]; // item for a given obs
##   int<lower=0> subject[N]; // subject for a given obs
##   int<lower=0> trial[N]; // trial for a given obs
## }
## 
## parameters {
##   real A; // = log_A, to be exponentialted later
##   real A_es[ns]; 
##   real A_ei[ni]; 
##   //real A_esi[ns,ni]; 
##   real A_esi[nsi];
##   real<lower=0> sigma_A_ei;
##   real<lower=0> sigma_A_es; 
##   real<lower=0> sigma_A_esi; 
## 
##   real B; // = log_B, to be exponentialted later
##   real B_es[ns]; 
##   real B_ei[ni]; 
##   //real B_esi[ns,ni]; 
##   real B_esi[nsi]; 
##   real<lower=0> sigma_B_ei; 
##   real<lower=0> sigma_B_es; 
##   real<lower=0> sigma_B_esi; 
## 
##   real T; 
##   real T_es[ns]; 
##   real T_ei[ni]; 
##   //real T_esi[ns,ni]; 
##   real T_esi[nsi];
##   real<lower=0> sigma_T_ei; 
##   real<lower=0> sigma_T_es; 
##   real<lower=0> sigma_T_esi; 
## 
##   real R; 
##   real R_es[ns]; 
##   real R_ei[ni]; 
##   //real R_esi[ns,ni]; 
##   real R_esi[nsi];
##   real<lower=0> sigma_R_ei; 
##   real<lower=0> sigma_R_es; 
##   real<lower=0> sigma_R_esi; 
## 
##   // add sigma variability 
## 
##   real<lower=0> sigma;
## }
## 
## transformed parameters {  
##   real y_hat[N];
##   real Alpha;
##   real Beta;// = B + B_es[subject[i]] + B_ei[item[i]] + B_esi[subject[i], item[i]];
##   real log_Rate;// = R + R_es[subject[i]] + R_ei[item[i]] + R_esi[subject[i], item[i]];
##   real log_Tau;// = T + T_es[subject[i]] + T_ei[item[i]] + T_esi[subject[i], item[i]];
## 
##   for(i in 1:N){ 
##     Alpha = exp(A + A_es[subject[i]] + A_ei[item[i]] + A_esi[si_lookup[subject[i], item[i]]]);
##     Beta = exp(B + B_es[subject[i]] + B_ei[item[i]] + B_esi[si_lookup[subject[i], item[i]]]);
##     log_Rate = R + R_es[subject[i]] + R_ei[item[i]] + R_esi[si_lookup[subject[i], item[i]]];
##     log_Tau = T + T_es[subject[i]] + T_ei[item[i]] + T_esi[si_lookup[subject[i], item[i]]];
##     // Tau = exp(Tau*Rate)-2; // old transformed version
##     // print(log_Alpha[i]);
##     // print(log_Beta[i]);
##     // print(Tau[i]);
##     // print(Rate[i]);
##     // print(exp(log_Alpha[i]) + exp(log_Beta[i]) * (Tau[i]+1) / (Tau[i] + trial[i]^Rate[i]));
##     // print(log(exp(log_Alpha[i]) + exp(log_Beta[i]) * (Tau[i]+1) / (Tau[i] + trial[i]^Rate[i])));
##     // print("");
##     y_hat[i] =  log(Alpha + Beta * (exp(log_Tau) + 1)/(exp(log_Tau) + exp(exp(log_Rate)*trial[i])));
##     // this resulted in no delayed start ever... : log(exp(log_Alpha) + (exp(log_Beta) * (exp(log_Tau) + 1) /(exp(log_Tau) + exp(log_Rate)*trial[i])));
##     // **old transformed version** log(exp(log_Alpha) + exp(log_Beta) * (Tau+1) / (Tau + trial[i]^Rate));
##     // go back to original version, but constrain Tau, Rate to be positive 
##   }
## }
## 
## model {
##   sigma ~ exponential(.1);
## 
##   A ~ normal(0, 6); // set as overall mean and sd of data
##   B ~ normal(8, 5); // set as mean, sd for retrieval trials
##   T ~ normal(5, 10); // was centered on 0
##   R ~ normal(-1, 2);
## 
##   sigma_A_es ~ exponential(1); 
##   sigma_A_ei ~ exponential(1);
##   sigma_A_esi ~ exponential(1);
## 
##   sigma_B_es ~ exponential(1);
##   sigma_B_ei ~ exponential(1);
##   sigma_B_esi ~ exponential(1);
## 
##   sigma_R_es ~ exponential(1);
##   sigma_R_ei ~ exponential(1);
##   sigma_R_esi ~ exponential(1);
## 
##   sigma_T_es ~ exponential(1);
##   sigma_T_ei ~ exponential(1);
##   sigma_T_esi ~ exponential(1);
##   
##   A_es ~ normal(0, sigma_A_es);
##   A_ei ~ normal(0, sigma_A_ei);
##   A_esi ~ normal(0, sigma_A_esi);
##   // for(i in 1:ns) {
##   //   for(j in 1:ni)
##   //     A_esi[i,j] ~ normal(0, sigma_A_esi);
##   // }
## 
##   B_es ~ normal(0, sigma_B_es);
##   B_ei ~ normal(0, sigma_B_ei);
##   B_esi ~ normal(0, sigma_B_esi);
##   // for(i in 1:ns) {
##   //   for(j in 1:ni)
##   //     B_esi[i,j] ~ normal(0, sigma_B_esi);
##   // }
## 
##   R_es ~ normal(0, sigma_R_es);
##   R_ei ~ normal(0, sigma_R_ei);
##   R_esi ~ normal(0, sigma_R_esi);
##   // for(i in 1:ns) {
##   //   for(j in 1:ni)
##   //     R_esi[i,j] ~ normal(0, sigma_R_esi);
##   // }
## 
##   T_es ~ normal(0, sigma_T_es);
##   T_ei ~ normal(0, sigma_T_ei);
##   T_esi ~ normal(0, sigma_T_esi);
##   // for(i in 1:ns) {
##   //   for(j in 1:ni)
##   //     T_esi[i,j] ~ normal(0, sigma_T_esi);
##   // }
## 
##   y ~ normal(y_hat, sigma); 
## }
## generated quantities {
##   vector[N] logLik; 
##   for(n in 1:N){
##     logLik[n] = normal_lpdf(y[n] | y_hat[n], sigma);
##   }
## }

Model Fit to Data

Diagnostics

Rhat distribution

Rhats for component parameters

Each spike represents the R-hat value for a particular component parameter. Below, very high values are examined more closely.

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Extreme Rhat values (z.score(Rhat) > 1.75)

Parameter param mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat Rhat.z
Alpha A_esi[178] 0.1528006 0.0578721 0.1310679 -0.1292053 0.0688531 0.1624331 0.2472850 0.3816242 5.129252 1.338995 2.953078
Alpha A_esi[213] 0.1883704 0.0782230 0.1427972 -0.1334271 0.1060492 0.2110088 0.2874058 0.4168864 3.332497 1.647783 6.260338
Alpha A_esi[27] 0.0609863 0.0918136 0.1739487 -0.2493913 -0.0794928 0.0581416 0.2031400 0.3543799 3.589454 1.628272 6.051369
Beta B_es[13] -0.1770123 0.0310945 0.0895481 -0.3495303 -0.2317515 -0.1759894 -0.1185680 -0.0064319 8.293639 1.266047 2.171779
Beta B_es[15] -0.1228044 0.0249546 0.1012218 -0.2983781 -0.1906058 -0.1369978 -0.0659538 0.1137506 16.453022 1.232229 1.809567
Beta B_es[30] -0.1190415 0.0265075 0.0844687 -0.2846279 -0.1755116 -0.1198513 -0.0601198 0.0392172 10.154364 1.233612 1.824381
Log Posterior lp__ 5370.5209983 84.7640565 176.2218952 5105.4142170 5242.4500740 5355.1086325 5479.2603044 5781.7119056 4.322114 2.100838 11.112754
Rate R_es[15] 0.2299083 0.4408033 0.7935105 -1.1259960 -0.5412067 0.4019762 0.9387771 1.3635766 3.240527 1.930861 9.292230
Rate R_es[29] 0.6544375 0.1491148 0.4046219 -0.1990594 0.3281066 0.7592682 0.9243157 1.3836030 7.363043 1.470547 4.362063
Rate R_es[3] 0.7291509 0.1059177 0.2908746 0.1920788 0.5404653 0.7058102 0.9159891 1.3472402 7.541793 1.346481 3.033264
Rate R_es[5] -1.1304937 0.1657355 0.6672449 -2.2166805 -1.6264138 -1.3129994 -0.6138894 0.1657230 16.208381 1.250619 2.006537
Rate R_esi[109] -0.0974086 0.1414697 0.2649148 -0.5016366 -0.3041247 -0.1491588 0.0892327 0.5003235 3.506592 1.729870 7.139530
Rate R_esi[121] -0.1338524 0.0727463 0.1976933 -0.4577024 -0.2628953 -0.1635148 -0.0373821 0.3571796 7.385198 1.315517 2.701619
Rate R_esi[13] -0.1269262 0.0727528 0.1977566 -0.4794831 -0.2850213 -0.1203227 -0.0021226 0.2774594 7.388612 1.309825 2.640655
Rate R_esi[145] -0.2902321 0.0893930 0.2366871 -0.6910108 -0.4693277 -0.3109885 -0.1377721 0.2389899 7.010392 1.364337 3.224501
Rate R_esi[178] 0.3635148 0.1248837 0.2529031 -0.1416398 0.1914777 0.3851694 0.5468294 0.8007838 4.101070 1.490434 4.575056
Rate R_esi[213] -0.0239842 0.1997790 0.3448358 -0.7047983 -0.2834701 0.0555124 0.2384631 0.5108027 2.979376 1.796669 7.854972
Rate R_esi[27] -0.3512084 0.0765492 0.1931216 -0.6984287 -0.4895754 -0.3547326 -0.2275097 0.0191313 6.364733 1.324413 2.796905
Rate R_esi[5] -0.1301388 0.0521256 0.2592350 -0.6618646 -0.2976963 -0.1314962 0.0469936 0.3528312 24.733501 1.239540 1.887870
Rate R_esi[8] 0.2612065 0.2335212 0.5939500 -0.6755302 -0.2808781 0.3140437 0.7637026 1.2549159 6.469146 1.341625 2.981253
Sigma sigma_B_esi 0.0305271 0.0076675 0.0151755 0.0073465 0.0187892 0.0263785 0.0416571 0.0628671 3.917179 1.918590 9.160799
Sigma sigma_T_ei 0.4050245 0.0911716 0.3193876 0.0443615 0.1840105 0.3096348 0.5477224 1.2738183 12.272038 1.319134 2.740359
Sigma sigma_T_esi 2.0678775 0.0688242 0.3002637 1.5137520 1.8670463 2.0553590 2.2708286 2.6418036 19.033734 1.247863 1.977015
Tau T 23.8535473 2.1530226 3.9948446 16.0259324 21.2129774 23.3844121 27.2410927 30.6917108 3.442727 1.820588 8.111160
Tau T_es[1] -20.4749820 2.1896434 4.0881503 -27.0891333 -24.1573974 -20.5786560 -17.1123726 -12.8726208 3.485836 1.769170 7.560449
Tau T_es[11] -20.4016708 2.3522768 4.5592827 -27.5928285 -24.3406129 -20.0467053 -17.3453876 -11.8535056 3.756784 1.667245 6.468783
Tau T_es[12] -0.6214949 2.2479174 6.3338921 -15.1779521 -4.6214803 0.0319130 3.8943624 9.5399011 7.939271 1.257164 2.076634
Tau T_es[13] 21.6531526 3.6339156 12.2278786 0.6402405 13.7129719 20.9200230 27.1539909 52.3350859 11.322767 1.252643 2.028216
Tau T_es[15] 2.5774934 7.5637385 15.9405076 -21.2803307 -11.9408669 1.5737435 15.1908961 29.9265677 4.441516 1.628849 6.057541
Tau T_es[20] -15.8989340 1.7779317 6.2625115 -26.1629093 -20.9263004 -16.0031559 -11.9487682 -2.3030194 12.407004 1.291724 2.446789
Tau T_es[24] -27.1840065 2.9688276 7.0709213 -43.7298344 -31.4064699 -24.9899136 -22.1674132 -16.7840537 5.672599 1.647359 6.255795
Tau T_es[26] -15.1759179 1.9949027 7.4141247 -26.6184711 -20.6528700 -15.3389129 -12.2530876 2.5509217 13.812629 1.280523 2.326819
Tau T_es[28] -19.8071586 2.1666361 4.1731653 -26.4430990 -23.4760275 -19.7276313 -16.6322347 -11.7035234 3.709874 1.740413 7.252444
Tau T_es[29] 14.9829372 6.2569257 15.0624283 -11.3536500 3.9256568 14.3589683 23.7244701 45.7895308 5.795194 1.506951 4.751966
Tau T_es[3] 24.3081403 4.4516776 11.6606364 5.9970220 15.2433278 23.0240959 33.9518306 48.1309724 6.861153 1.448437 4.125255
Tau T_es[30] -15.6189553 2.2332361 4.7894186 -23.6488082 -19.4685196 -15.4023624 -12.4252651 -5.6216652 4.599348 1.591956 5.662401
Tau T_es[4] -17.6077361 1.8862021 4.5730241 -25.0268070 -21.3688885 -17.8048811 -14.1384636 -8.4266948 5.878013 1.541530 5.122320
Tau T_es[5] -11.0453403 3.6334025 10.1961349 -23.4936406 -18.8786125 -14.1087767 -5.6840119 12.7572096 7.874883 1.393800 3.540062
Tau T_es[6] -12.3758259 2.2351473 5.1117202 -21.2198507 -16.2136392 -12.1620077 -9.0314097 -2.2858427 5.230243 1.484762 4.514312
Tau T_es[7] -17.9045159 2.2429018 4.3909176 -25.6737977 -21.6300124 -17.4599784 -14.5351956 -9.9576163 3.832569 1.627479 6.042872
Tau T_es[8] -10.4910888 1.9525864 4.9571072 -19.2105983 -13.8036909 -10.8614252 -7.8093746 -0.4684246 6.445195 1.276945 2.288500
Tau T_es[9] -17.1972930 2.0258440 4.2490178 -25.5740827 -20.3899276 -16.7079521 -14.4982015 -8.4031933 4.399113 1.562417 5.346031